
 Proposal for an Algorithm wich determines the minimal
 necessary conditions for having invariant Quotients
 of the kind A215940.
 
 Introduction:

Let us assume that you have computed N! permutations
for the digits in base N, and you want to check which
is the smallest radix or base from where all the
quotients in A215940 have identical expressions
for each next base.
 
 Informal description (Below):
 
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  Step 1.- Set r0=N, r1= N+1, two radices or bases to test for the equality in the
  generalized quotients of A215940.
  
  Step 2.- Compute the quotients for both base r0 and baser r1.
  
  Step 3.- Compare them, IF at least one of the quotients looks different
  in one of these two bases:
  
    ia) Set r0=r1 and increment r1 by 1, then
   iia) Iterate from the Step 2.
   
  ELSE, if the quotients are identical between these two bases:
  
    ib) (weak induction) pick some k arbitrarily greater than r1.
   iib) Compute the quotients for each base among (r1+1) and k.
   
  iiib) IF the corresponding quotients by offset look indentical in
        all of these other bases then r0 might be considered the lower
        bound for the Universality of the quotiens, so we can proceed
        with the netx step.
        
  ELSE Go back and run the steps (ia) and (iia).
  
  Step 4. FINISH the execution. (End)
  
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R. J. Cano, Jan 21th 2013.

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